"I was somewhat fascinated by the similarities that arose between a particular fictional girl and me."

or is it "...the fictional girl and myself?"

In this sentence, you should use "myself" because it's referring to the subject: "I" These are called reflexive pronouns.

thank you

You're welcome. =)

To determine whether to use "me" or "myself" in this sentence, you can follow a simple rule.

First, try removing the other person or subject in the sentence. In this case, you would remove the phrase "that arose between a particular fictional girl and":

"I was somewhat fascinated by the similarities that arose... me."

Now, replace "me" with "myself" and see if it still makes sense:

"I was somewhat fascinated by the similarities that arose... myself."

In this case, "myself" doesn't fit and sounds grammatically incorrect. Therefore, the correct choice is to use "me":

"I was somewhat fascinated by the similarities that arose between a particular fictional girl and me."

Using "myself" would be incorrect because "myself" is a reflexive pronoun and should only be used when the subject of the sentence is also the object of the verb or preposition. In this case, "me" is the appropriate pronoun to use.